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What is the greatest distance between two points in a

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rajathpanta
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What is the greatest distance between two points in a [#permalink] New post  Updated on: 30 Oct 2012, 09:45
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What is the greatest distance between two points in a cylinder where the area of the base is 9 pi and height is 5?

A. \(\sqrt{34}\)
B. \(\sqrt{48}\)
C. \(\sqrt{61}\)
D. \(\sqrt{76}\)
E. \(\sqrt{106}\)
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Originally posted by rajathpanta on 30 Oct 2012, 09:09.
Last edited by Bunuel on 30 Oct 2012, 09:45, edited 1 time in total.
Renamed the topic and edited the question.
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Re: What is the greatest distance b/w 2 points [#permalink] New post  30 Oct 2012, 09:21
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rajathpanta wrote:
What is the greatest distance b/w 2 points in a cylinder where the area of the base is 9 pi and the height is 5-

a)\(\sqrt{34}\)
b)\(\sqrt{48}\)
c)\(\sqrt{61}\)
d)\(\sqrt{76}\)
e)\(\sqrt{106}\)


If radius of base is r then pi*r^2 = 9pi
=> r =3

The greatest distance would be between A and B. On different sides of circularr faces
=sqrt (6^2 +5^2)
=sqrt 61
Ans C it is.
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Re: What is the greatest distance b/w 2 points [#permalink] New post  30 Oct 2012, 09:43
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rajathpanta wrote:
What is the greatest distance b/w 2 points in a cylinder where the area of the base is 9 pi and the height is 5-

a)\(\sqrt{34}\)
b)\(\sqrt{48}\)
c)\(\sqrt{61}\)
d)\(\sqrt{76}\)
e)\(\sqrt{106}\)


Look at the diagram below:
Attachment:
Cylinder.png
Cylinder.png [ 4.99 KiB | Viewed 9016 times ]
The greatest distance between two points would be x.

Now, since \(area=9\pi=\pi{r^2}\), then \(r=3\)and \(d=6\) --> \(x=\sqrt{5^2+6^2}=\sqrt{61}\).

Answer: C.

Hope it's clear.

P.S. Please do not shorten the words in the question. Thank you.
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Re: What is the greatest distance between two points in a [#permalink] New post  06 Oct 2017, 10:57
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rajathpanta wrote:
What is the greatest distance between two points in a cylinder where the area of the base is 9 pi and height is 5?

A. \(\sqrt{34}\)
B. \(\sqrt{48}\)
C. \(\sqrt{61}\)
D. \(\sqrt{76}\)
E. \(\sqrt{106}\)


We see that the greatest distance in a cylinder is a diagonal line from one base to the other, or in other words, the hypotenuse of a right triangle, with the height of the cylinder being the height of the triangle and the diameter of the base being the base of the triangle. Let’s determine the diameter.

Since the area of the base is 9π:

area = πr^2

9π = πr^2

9 = r^2

3 = r

So, the diameter is 6. Recall that the height of the cylinder is 5, so we can determine the length of the diagonal using the Pythagorean theorem:

6^2 + 5^2 = d^2

36 + 25 = d^2

61 = d^2

√61 = d

Answer: C
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Re: What is the greatest distance between two points in a [#permalink] New post  02 Jun 2019, 10:36
rajathpanta wrote:
What is the greatest distance between two points in a cylinder where the area of the base is 9 pi and height is 5?

A. \(\sqrt{34}\)
B. \(\sqrt{48}\)
C. \(\sqrt{61}\)
D. \(\sqrt{76}\)
E. \(\sqrt{106}\)


given
pi * r^2 = 9 * pi
r=3
d= 6
so longest poin t; √36+25 ; √61
IMO C
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Re: What is the greatest distance between two points in a [#permalink] New post  06 Nov 2023, 06:04
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